I remember my lesson at my fingertips. Is it correct?
I have learnt my lesson by heart. Is this the only sentence we can use here?
I have memorized my lesson by heart. Is it also correct?
If a student has learnt his lesson very well by heart, how will you say in English?
You can say that you have information at your fingertips, but not a lesson.
I have memorised the contents of that lesson.
I know the contents of that lesson by heart.
I have the information about the train timetable at my fingertips.
To have something "at your fingertips" simply means that you can bring the information out instantly without thinking about it. You might have had to memorise it or it might just be something you know, like your date of birth.
Remember - correct capitalisation, punctuation and spacing make posts much easier to read.